https://file.aiquickdraw.com/mathbot/file/1729564281669wacu4xot.jpg

Let's break down the problem step by step based on the image you uploaded:

### Problem Summary:

- **Paint Can A** has \( \frac{1}{2} \) pint of green paint, made of yellow and blue paint mixed in a ratio of **1:1**.
- **Paint Can B** also contains \( \frac{1}{2} \) pint of green paint, but here the yellow and blue paint are mixed in the ratio of **2:1**.
- These two cans are mixed together to form **one pint** of green paint.

### Part a. 
**Which color will represent a larger fraction or percent of the new can of paint?**

1. **Paint Can A:** 
   - Since the yellow and blue paint are mixed in a 1:1 ratio, the \( \frac{1}{2} \) pint contains \( \frac{1}{4} \) pint of **yellow** and \( \frac{1}{4} \) pint of **blue**.

2. **Paint Can B:** 
   - The yellow and blue paint are mixed in a 2:1 ratio, so for the \( \frac{1}{2} \) pint of paint, we can break it down:
     - \( \frac{2}{3} \) of the can is yellow paint, which equals \( \frac{1}{3} \) pint.
     - \( \frac{1}{3} \) of the can is blue paint, which equals \( \frac{1}{6} \) pint.

Now, after mixing these two cans together, the total amount of yellow and blue will be:

- **Yellow Paint:**
  - \( \frac{1}{4} \) (from Can A) + \( \frac{1}{3} \) (from Can B) = \( \frac{3}{12} + \frac{4}{12} = \frac{7}{12} \) pint of yellow paint.

- **Blue Paint:**
  - \( \frac{1}{4} \) (from Can A) + \( \frac{1}{6} \) (from Can B) = \( \frac{3}{12} + \frac{2}{12} = \frac{5}{12} \) pint of blue paint.

Thus, **yellow paint** represents a larger fraction of the new can of paint, since \( \frac{7}{12} \) is greater than \( \frac{5}{12} \).

### Part b. 
**Determine the ratio of yellow to blue paint in the big pint-sized paint can.**

From our calculations above, we know:
- There are \( \frac{7}{12} \) pint of yellow paint.
- There are \( \frac{5}{12} \) pint of blue paint.

The ratio of yellow to blue paint is therefore \( \frac{7}{12} : \frac{5}{12} \), which simplifies to \( 7:5 \).

---

Would you like more detailed steps for part b, or do you have any questions? Here are some related questions you could explore:

1. What would the ratio be if Paint Can B had a different yellow-to-blue ratio, such as 3:2?
2. How would the overall fraction of blue paint change if Can A had more blue than yellow?
3. How does changing the quantity of paint in one can affect the overall color ratio?
4. Could the new paint mixture be made to have an equal amount of yellow and blue? How?
5. What if Paint Can A was only \( \frac{1}{4} \) pint? How would the total mixture ratio change?

**Tip:** Ratios can be simplified by finding the greatest common divisor of the quantities involved.

Paint Can A is 1/2 pint of green paint that is made up of yellow and blue paint mixed together in the ratio 1:1. Paint Can B is also 1/2 pint of green paint, but the yellow and blue paint are mixed together in the ratio 2:1. The two cans get mixed together to make one big pint-sized paint can.

A) Which color will represent a larger fraction or percent of the new can of paint? Explain how you know.
B) Determine the ratio of yellow to blue paint in the big pint-sized paint can.

Learn how to solve a problem involving mixing two cans of paint with different yellow-to-blue ratios. This step-by-step solution covers key mathematical concepts such as simplifying ratios and adding fractions, suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation